QQuestion
If 1701 is the nth term of the Geometric Progression 7, 21, 63, …, find:
(a) the value of n.
(b) hence, the sum of the n terms of the G.P.
ICSEClass 10MathematicsArithmetic And Geometric Progression04 Mark2025 Moderate
✓Answer
First term, a = 7
Common ratio, r = 21 ÷ 7 = 3
(a) The nth term of a G.P. is Tₙ = arⁿ⁻¹.
⇒ 1701 = 7 × 3ⁿ⁻¹
⇒ 3ⁿ⁻¹ = 1701 ÷ 7
⇒ 3ⁿ⁻¹ = 243
⇒ 3ⁿ⁻¹ = 3⁵
⇒ n − 1 = 5
⇒ n = 6
(b) Sum of n terms of a G.P. = \mathrm{S}_{\mathrm{n}}=\frac{\mathrm{a}(\mathrm{r}^{\mathrm{n}}-1)}{\mathrm{r}-1}
\mathrm{S}_6=\frac{7(3^6-1)}{3-1}= \frac{7(729-1)}{2}
= \frac{7\times728}{2}
= 7 × 364
= 2548
Therefore, n = 6 and the sum of the first six terms is 2548.
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